The process e thorn e- -> sigma thorn sigma over bar - is studied from threshold up to 3.04 GeV=c2 via the initial -state radiation technique using data with an integrated luminosity of 12.0 fb-1, collected at center-of-mass energies between 3.773 and 4.258 GeV with the BESIII detector at the BEPCII collider. The pair production cross sections and the effective form factors of sigma are measured in eleven sigma thorn sigma over bar - invariant mass intervals from threshold to 3.04 GeV=c2. The results are consistent with the previous results from Belle and BESIII. Furthermore, the branching fractions of the decays J=psi ->sigma thorn sigma over bar - and psi o3686 thorn -> sigma thorn sigma over bar - are determined and the obtained results are consistent with the previous results of BESIII.